Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Identify and define key algebraic terms (variable, constant, coefficient, term, expression).
• Write algebraic expressions from real-world situations.
• Simplify algebraic expressions by combining like terms.
• Solve simple one-step equations using inverse operations.

Lesson summary

This week, we begin our journey into the exciting world of algebra! Algebra is a powerful tool that helps us solve problems where some information is unknown. It's like being a detective, using clues (called equations and expressions) to find the missing pieces of a puzzle. Imagine you're helping your family budget for groceries. Algebra can help you figure out how much money you have left after buying certain items or how many of a specific item you can afford. Or, if you're planning a soccer tournament, algebra can help you calculate the number of teams needed based on the number of players.

Lesson notes

2.1 What are Algebraic Expressions? An algebraic expression is a combination of numbers, variables, and operation symbols (+, -, ×, ÷).

Variable: A letter or symbol (like x, y, or a) that represents an unknown number. Think of it as a placeholder for a value we haven't found yet.

Constant: A number that has a fixed value. For example, 5, -3, or ½ are constants.

Coefficient: A number that is multiplied by a variable. In the expression 3x, 3 is the coefficient.

Expression: A collection of terms separated by + or - signs.

Example: 2x + 5y -

3. Example: In the expression `4a + 7 - 2b`, `a` and `b` are variables. 4 and -2 are coefficients. 7 is a constant. `4a`, `7`, and `-2b` are terms. 2.2 Writing Algebraic Expressions from Word Problems Being able to translate words into algebraic expressions is a crucial skill. Look for keywords like "sum," "difference," "product," and "quotient." "Sum" means addition (+). "Difference" means subtraction (-). "Product" means multiplication (× or implied). "Quotient" means division (÷).

Example 1: "The sum of a number and five" can be written as `x + 5`.

Example 2: "Three times a number decreased by two" can be written as `3y - 2`.

Example 3: "The quotient of a number and four, increased by one" can be written as `(z / 4) + 1`. 2.3 Simplifying Algebraic Expressions: Combining Like Terms Like terms are terms that have the same variable raised to the same power. You can only combine like terms by adding or subtracting their coefficients.

Example 1: Simplify `3x + 5x - 2x`. All the terms have the variable `x`, so they are like terms. `3x + 5x - 2x = (3 + 5 - 2)x = 6x` Example 2: Simplify `4y + 2 - y + 6`.

Identify like terms: `4y` and `-y` are like terms; `2` and `6` are like terms. `4y + 2 - y + 6 = (4y - y) + (2 + 6) = 3y + 8` Example 3: Simplify `5a + 3b - 2a + b - 4`.

Identify like terms: `5a` and `-2a` are like terms; `3b` and `b` are like terms; `-4` is a constant. `5a + 3b - 2a + b - 4 = (5a - 2a) + (3b + b) - 4 = 3a + 4b - 4` 2.4 Simple Equations An equation is a statement that two expressions are equal. It contains an equals sign (=). Our goal is to find the value of the variable that makes the equation true.

Example: `x + 3 = 7` is an equation. 2.5 Solving One-Step Equations Using Inverse Operations To solve an equation, we need to isolate the variable on one side of the equals sign. We do this by performing the inverse operation. Inverse operations "undo" each other. The inverse of addition is subtraction. The inverse of subtraction is addition. The inverse of multiplication is division. The inverse of division is multiplication.

Important Rule: Whatever you do to one side of the equation, you must do to the other side to keep the equation balanced.

Example 1: Solve `x + 5 = 12` The operation is addition (+5). The inverse operation is subtraction (-5).

Subtract 5 from both sides: `x + 5 - 5 = 12 - 5` `x = 7` Example 2: Solve `y - 3 = 8` The operation is subtraction (-3). The inverse operation is addition (+3).

Add 3 to both sides: `y - 3 + 3 = 8 + 3` `y = 11` Example 3: Solve `3z = 15` The operation is multiplication (3 × z). The inverse operation is division (÷3).

Divide both sides by 3: `3z / 3 = 15 / 3` `z = 5` Example 4: Solve `a / 4 = 2` The operation is division (a ÷ 4). The inverse operation is multiplication (×4).

Multiply both sides by 4: `(a / 4) × 4 = 2 × 4` `a = 8` Guided Practice (With Solutions)

Question 1: Write an algebraic expression for "Six less than twice a number." Solution: Let the number be represented by `n`. Twice the number is `2n`. Six less than twice the number is `2n - 6`.

Therefore, the algebraic expression is `2n - 6`.

Question 2: Simplify the expression `7p - 3 + 2p + 5 - p`.

Solution: Identify like terms: `7p`, `2p`, and `-p` are like terms; `-3` and `5` are like terms.

Group the like terms: `(7p + 2p - p) + (-3 + 5)` Combine the like terms: `8p + 2` Therefore, the simplified expression is `8p + 2`.

Question 3: Solve the equation `k + 9 = 15`.

Solution: The operation is addition (+9). The inverse operation is subtraction (-9).

Subtract 9 from both sides: `k + 9 - 9 = 15 - 9` `k = 6` Question 4: Solve the equation `2x = 18` Solution: The operation is multiplication (2 × x). The inverse operation is division (÷2).

Divide both sides by 2: `2x / 2 = 18 / 2` `x = 9` Independent Practice (Questions Only) Write an algebraic expression for "The product of a number and seven, increased by four." Write an algebraic expression for "A number divided by three, decreased by ten." Simplify the expression `5x + 2y - x + 3y - 1`. Simplify the expression `8a - 4b - 2a + b + 7`. Solve the equation `m - 6 = 4`. Solve the equation `y / 5 = 3`. Solve the equation `7 + x = 11`. Solve the equation `4p = 24`. Thando has x number of apples. Sindi has 3 more apples than Thando. Write an expression for the number of apples Sindi has. Sipho earns n Rands per hour. If he works 8 hours, write an expression for his total earnings.